Bernstein super fractal interpolation function for countable data systems.

We introduce a fractal operator on C [ 0 , 1 ] which sends a function f ∈ C (I) to fractal version of f where fractal version of f is a super fractal interpolation function corresponding to a countable data system. Furthermore, we study the continuous dependence of super fractal interpolation functions on the parameters used in the construction. We know that the invariant subspace problem and the existence of a Schauder basis gained lots of attention in the literature. Here, we also show the existence of non-trivial closed invariant subspace of the super fractal operator and the existence of fractal Schauder basis for C (I) . Moreover, we can see the effect of the composition of Riemann-Liouville integral operator and super fractal operator on the fractal dimension of continuous functions. We also mention some new problems for further investigation. [ABSTRACT FROM AUTHOR]